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On formulas for moments of the Wishart distributions as weighted generating functions of matchings

Abstract : We consider the real and complex noncentral Wishart distributions. The moments of these distributions are shown to be expressed as weighted generating functions of graphs associated with the Wishart distributions. We give some bijections between sets of graphs related to moments of the real Wishart distribution and the complex noncentral Wishart distribution. By means of the bijections, we see that calculating these moments of a certain class the real Wishart distribution boils down to calculations for the case of complex Wishart distributions.
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Yasuhide Numata, Satoshi Kuriki. On formulas for moments of the Wishart distributions as weighted generating functions of matchings. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.953-964. ⟨hal-01186264⟩

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